It's not fun having a dog who is anti-cat with a cat. We lived with that for 10 years. They had to be separated all that time. Even when we were home, dog got the bottom two levels of our house, cat got the upper two. When we were not home we had a gate across the entrance to the basement. I wish I could tell you a process but we never found anything that worked. This dog was fine with cats not our own, our Vet said she even cuddled with the clinic cats.
Your dog is perfectly aware that a cat is not a small dog or a bunny but that might not matter. There is just no way you can tell ahead how this is going to work long term. Some rescues will let you try an animal out to see how introductions go. It does not sound ideal though, when the dog is already showing signs of aggression to small animals. You might find no one will let you take a cat.